In this paper, we deal with the Byzantine-robust decentralized stochastic optimization problem over static and time-varying networks. We introduce the TV norm penalty to handle Byzantine attacks and propose a stochastic subgradient method to solve the penalized problem. Theoretical analysis and numerical experiments demonstrate the robustness of our proposed method to Byzantine attacks, no matter the network topology is static or time-varying. In our future work, we will investigate the application of variance reduction techniques, which have been shown effective in Byzantine-robust centralized stochastic optimization [1]}, to the decentralized case. We will also consider TV norm penalties based on \(\ell _2\)  and \(\ell _\infty \)  norms [2]}.
